Prep: Preheat your oven to 375°F (190°C). Grease a 9x13-inch (or oval) baking dish with a little olive oil.
Slice: Using a mandoline or sharp knife, slice all vegetables into 1/8-inch thick rounds.
Infuse: In a small saucepan over medium-low heat, combine the cream, garlic, and thyme. Simmer for 3–5 minutes. Season with salt and pepper.
Assemble: Arrange the vegetable slices in the prepared dish in vertical, overlapping rows, alternating colors (Sweet Potato -> Parsnip -> Beet).
Pour: Pour the cream mixture evenly over the vegetables. Drizzle with 2 tbsp olive oil.
Cheese: Sprinkle the Gruyère and Parmesan over the top.
Bake: Cover with foil and bake for 35–40 minutes. Remove foil and bake for another 15–25 minutes until the top is golden and vegetables are tender.
Rest: Let the dish rest for 10 minutes before serving to allow the sauce to set.